(1) Field of the Invention
The invention relates to a multiplying circuit for multiplying a first signal x(t) by a periodic second signal y(t). It is particularly suitable for use as an amplitude demodulator in a stereo decoder or in a phase-locked loop (PLL) and comprises circuits constructed with switched capacitors.
(2) Description of the Prior Art
As is known, an amplitude demodulator has for its function to convert a band-limited signal s(nf.sub.o ;t) whose frequency spectrum is located in a frequency band extending from the frequency (nf.sub.o -f.sub.1)Hz to a frequency (nf.sub.o +f.sub.1)Hz, into an AF-signal x(n;t) whose frequency spectrum is located in the frequency band extending from the frequency 0 Hz to the frequency f.sub.1 Hz. The last-mentioned frequency band will be called AF-band (Audio Frequency band) hereinafter. In the foregoing both f.sub.o and F.sub.1 are a fixed frequency and n is an integer.
In practice x(nf.sub.o ;t) will form part of a signal x'(t) which in principle is formed by an infinite number of frequency-stacked band-limited signals. As usually only one of these band-limited signals must be translated to the AF-band (for example only the signal x(f.sub.o ;t)), the amplitude demodulator comprises what is commonly denoted as a pre-modulation filter to which x'(t) is applied and which converts it into a signal x(t) which comprises only a limited number, for example N, of these band-limited signals. Let it now be assumed that each of these band-limited signals can be written as: EQU x(nf.sub.o ;t)=x(n;t) sin (2.pi.nf.sub.o t+.phi..sub.n)
When now x(t) is multiplied by a periodic carrier signal y(t) which satisfies, for example, the expression: EQU y(t)=2 sin (2.pi.f.sub.o t+.phi..sub.1)
a product signal z(t) is obtained which in addition to the AF-signal x(1;t) located in the AF band comprises N-2 further signals located around multiples of the frequency f.sub.o. When this signal z(t) is now applied to a post-modulation filter the signals located around these multiples of f.sub.o can be suppressed so that this filter supplies the AF-signal z(1;t) as an output signal.
If the carrier signal y(t) were indeed of a purely sinusoidal shape and the multiplying circuit were to operate in a purely linear way, then only the signal x(1;t) would indeed occur in the AF band. In practice, however, it was found to be impossible to produce a purely linear multiplying circuit in a simple and cheap way. It was also found to be impossible to generate a purely sinusoidally varying carrier signal in a simple way. The result thereof is that in this demodulation procedure noise signals are also introduced in the AF-band, which signals may be particularly annoying.
In order to prevent these noise signals from occurring it is at present general practice to feed into stereo decoders a carrier signal which in contrast to the above mentioned sinusoidally varying carrier signal is not amplitude-continuous but which is amplitude-discrete and consequently can only assume a limited number of predetermined amplitude values. This may result in the carrier signal y(t) not comprising certain components whose frequencies are an integral multiple of f.sub.o, so that those signals x(nf.sub.o ;t) located around those frequencies do not arrive in the AF-band.
A particularly advantageous multiplying circuit of this type is described in Reference 1. It comprises N-signal channels each receiving the first signal x(t) via a signal input. Each signal channel includes a switching circuit having a control input for receiving control pulses. More specifically the control input of the switching circuit included in the signal channel having number k receives control pulses d(k,i), where k=0, 1, 2, . . . , N-1 and i=. . . -2, -1, 0, 1, 2, 3, . . . . In addition, each signal channel comprises, arranged in cascade with the switching circuit, a weighting network having a constant weighting factor W(k)=y(t.sub.o +k(T.sub.o /N), where T.sub.o represents a constant, and a pulse-reshaping circuit for converting a pulse applied thereto into a pulse whose width is not more than equal to 1/f.sub.o. Each signal channel supplies a channel signal consisting of a sequence of pulses whose amplitudes are equal to the product of the first signal x(t) and the constant weighting factor and whose width is determined by the pulse-reshaping circuit. The channel signals thus obtained are added together in an adder to form the desired product signal.
The N sequences of control pulses d(k;i) with which the switching circuits are controlled, are generated by a control pulse generator circuit of such a construction that each sequence of control pulses is periodic and has a repetition period T.sub.o =1/f.sub.o, and any control pulse d(k;i) occurs at the instant t.sub.o +k(T.sub.o /N)+iT.sub.o.
In a particularly advantageous embodiment of this multiplying circuit each signal channel comprises a capacitor having a capacitance C(k) which together with the associated switching circuit forms part of a circuit comprising a switched capacitor. This last-mentioned circuit is further followed by an operational amplifier which is shunted by a capacitor having a capacitance C and functions as a pulse-reshaping circuit. In this signal channel the weighting network is formed by the series arrangement of the two capacitors and the weighting factor W(k) of this weighting network is equal to the ratio C(k)/C of the two capacitances. In a practical embodiment of this multiplying circuit the operational amplifier and the capacitor shunting it are used in common for all signal channels and it then also functions as an adder device.
For this arrangement it is assumed that the pulse duration of the pulses of which the channel signal consists is only determined by the pulse-reshaping circuit and that the control pulses d(k;i) represent delta (dirac) pulses. In practice this ideal situation can, however, not be realized as the switching circuit has a resistance which is too high to be disregarded. As a result thereof a certain time is required, (charging time constant) to charge the capacitor C(k) to a value corresponding to the instantaneous value of the information signal x(t). This means that the switching circuit cannot be controlled directly by the sequence of delta pulses d(k;i) but that each delta pulse must be converted in a pulse-reshaping circuit into a control pulse g(k;i) of an adequate duration. As the sequence of control pulses g(k;i) thus obtained has a frequency spectrum which significantly deviates from that of the sequence of delta pulses, the frequency spectrum of the product signal also deviates significantly from the desired frequency spectrum. In practice this product signal was found to be further disadvantageously influenced by the fact that the switched capacitors C(k) in the different signal channels have different values. As a result thereof the charging time constants in the different signal channels are different.